"One thing is for sure: Hope never dies."

Now, should the 'h' in 'hope' be capitalized or not?
Thanks

I would say no if you are quoting someone.

I'm not quoting anyone. "Hope never dies" is my thesis statement. Knowing this, do you think I shouldn't capitalize it then?

Yes, you need the capital H on hope -- it's the beginning of an independent clause.

http://grammar.ccc.commnet.edu/grammar/marks/colon.htm

thanks. I thought so initially.

to help prevent pollution, people could walk, ride bikes, and use public transportation.

In the sentence you provided, the "h" in "hope" should not be capitalized. The general rule is that only the first letter of a sentence or a proper noun should be capitalized. "Hope" is a common noun, so it doesn't require capitalization unless it is at the beginning of a sentence or part of a title.